Line your 8×8 inch square baking pan with parchment paper or foil, leaving an overhang on the sides to make removing the fudge easier later.
Place the medium saucepan over low heat and pour in the sweetened condensed milk.
Add the creamy peanut butter to the saucepan.
Stir the mixture constantly with a silicone spatula, ensuring the peanut butter is fully incorporated into the milk.
Continue cooking over low heat for approximately 5 to 7 minutes, stirring continuously to prevent scorching at the bottom of the pan.
Remove the pan from the heat once the mixture is thick, glossy, and pulls away slightly from the sides of the saucepan.
Stir in the vanilla extract until fully combined.
Pour the mixture into your prepared baking pan, using the spatula to spread it into an even layer.
Place the pan in the refrigerator for at least 2 hours, or until the fudge is completely firm to the touch.
Lift the fudge out of the pan using the parchment paper edges and cut into 16 equal squares with a sharp knife.